Finite Group Databasebeta

← #11812952

Subgroups — #11812952

Order 1152.

1830 conjugacy classes of subgroups.

The subgroup lattice has 663 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#121C211yesmaximal, characteristic
2C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
3#10592921C211yesmaximal, characteristic, complemented
4#10592919C211yesmaximal, characteristic, complemented
5#10592919C211yesmaximal, characteristic, complemented
6#10592919C211yesmaximal, characteristic, complemented
7#10592919C211yesmaximal, characteristic, complemented
8#10592909C211yesmaximal, characteristic, complemented
9C2×#63658C211yesmaximal, characteristic, complemented
10#10592685C211yesmaximal, characteristic, complemented
11#10592677C211yesmaximal, characteristic, complemented
12#10592652C211yesmaximal, characteristic, complemented
13#10592651C211yesmaximal, characteristic, complemented
14#10592643C211yesmaximal, characteristic, complemented
15#10592642C211yesmaximal, characteristic, complemented
16#82656—34nomaximal
17C22×C32×D4C2211yescharacteristic
18C22×C32×D4C2211yescharacteristic
19C22×C32×D4C2211yescharacteristic
20C23×C32×C4C2211yescharacteristic
21C23×C3⋊Dic3C2211yescharacteristic
22C23×C3⋊Dic3C2211yescharacteristic
23C23×C3⋊Dic3C2211yescharacteristic
24C32×#121—24no—
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C32×C22⋊C4C2211yescharacteristic
28C2×#3757C2211yescharacteristic
29C2×#3757C2211yescharacteristic
30C2×#3757C2211yescharacteristic
31C2×#3757C2211yescharacteristic
32C2×#3757C2211yescharacteristic
33C2×#3757C2211yescharacteristic
34C2×#3757C2211yescharacteristic
35C2×#3757C2211yescharacteristic
36C2×#3757C2211yescharacteristic
37D4×C3⋊Dic3—24no—
38C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
39C2×#3750C2211yescharacteristic
40C2×#3750C2211yescharacteristic
41C2×C4×C3⋊Dic3C2211yescharacteristic
42#63658C2211yescharacteristic
43#63658C2211yescharacteristic
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48#63658C2211yescharacteristic
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52#63658C2211yescharacteristic
53#63658C2211yescharacteristic
54C2×C3×#121D314yes—
55C2×D4×Dic3—34no—
56#5222—34no—
57#5220—34no—
58#5220—34no—
59#5220—34no—
60#5220—34no—
61#5210—34no—
62C2×C3⋊#95—34no—
63#4986—34no—
64#4978—34no—
65#4953—34no—
66#4952—34no—
67#4944—34no—
68#4943—34no—
69C24×C32C2311yescharacteristic
70C24×C32C2311yescharacteristic
71C24×C32C2311yescharacteristic
72C2×C32×D4—22no—
73C2×C32×D4—22no—
74C2×C32×D4—22no—
75C2×C32×D4—22no—
76C2×C32×D4—22no—
77C2×C32×D4—22no—
78C2×C32×D4—22no—
79C2×C32×D4—41no—
80C2×C32×D4D414yes—
81C22×C32×C4—22no—
82C22×C32×C4—22no—
83C22×C32×C4—41no—
84C22×C32×C4C2311yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C3⋊Dic3—22no—
89C22×C3⋊Dic3—22no—
90C22×C3⋊Dic3—22no—
91C22×C3⋊Dic3—22no—
92C22×C3⋊Dic3—22no—
93C22×C3⋊Dic3—41no—
94C22×C3⋊Dic3—41no—
95C22×C3⋊Dic3—41no—
96C22×C3⋊Dic3—41no—
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C32×C4⋊C4—22no—
106C32×C22⋊C4—22no—
107C32×C22⋊C4—22no—
108#3757—22no—
109#3757—22no—
110#3757—22no—
111#3757—22no—
112#3757—41no—
113#3757—41no—
114#3757—41no—
115#3757—41no—
116#3757—41no—
117C4⋊(C3⋊Dic3)—22no—
118#3750—22no—
119#3750—41no—
120C4×C3⋊Dic3—22no—
121#2444—91noSylow
122C22×C3×D4C2×D314yes—
123C22×C3×D4C2×D314yes—
124C22×C3×D4C2×D314yes—
125C23×C3×C4C2×D314yes—
126C23×Dic3—34no—
127C23×Dic3—34no—
128C23×Dic3—34no—
129C3×#121—216no—
130C2×C3×C4⋊C4C2×D314yes—
131C2×C3×C22⋊C4C2×D314yes—
132C2×C3×C22⋊C4C2×D314yes—
133C2×#217—34no—
134C2×#217—34no—
135C2×#217—34no—
136C2×#217—34no—
137C2×#217—34no—
138C2×#217—34no—
139C2×#217—34no—
140C2×#217—34no—
141C2×#217—34no—
142D4×Dic3—616no—
143C2×C4⋊Dic3—34no—
144C2×Dic3⋊C4—34no—
145C2×Dic3⋊C4—34no—
146C2×C4×Dic3—34no—
147C3⋊#95—34no—
148C3⋊#95—34no—
149C3⋊#95—34no—
150C3⋊#95—34no—
151C3⋊#95—34no—
152C3⋊#95—34no—
153C3⋊#95—34no—
154C3⋊#95—34no—
155C3⋊#95—34no—
156C3⋊#95—34no—
157C3⋊#95—34no—
158C3⋊#95—34no—
159C23×C32—21no—
160C23×C32—21no—
161C23×C32—21no—
162C23×C32—21no—
163C23×C32—21no—
164C23×C32—21no—
165C23×C32—21no—
166C23×C32—21no—
167C23×C32—21no—
168C23×C32—21no—
169C23×C32—21no—
170C23×C32—21no—
171C23×C32—21no—
172C23×C32—21no—
173C23×C32—21no—
174C23×C32—21no—
175C23×C32—21no—
176C23×C32C2×D412yes—
177C23×C32C2×D412yes—
178C23×C32#4112yes—
179C23×C32#4112yes—
180C23×C32C2411yescharacteristic
181C32×D4—28no—
182C32×D4—44no—
183C32×D4—44no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4—21no—
188C2×C32×C4—21no—
189C2×C32×C4—21no—
190C2×C32×C4—21no—
191C2×C32×C4—21no—
192C2×C32×C4—21no—
193C2×C32×C4—21no—
194C2×C32×C4—44no—
195C2×C32×C4C2×D412yes—
196C2×C32×C4#4112yes—
197C2×C3⋊Dic3—21no—
198C2×C3⋊Dic3—21no—
199C2×C3⋊Dic3—21no—
200C2×C3⋊Dic3—21no—
201C2×C3⋊Dic3—21no—
202C2×C3⋊Dic3—21no—
203C2×C3⋊Dic3—21no—
204C2×C3⋊Dic3—21no—
205C2×C3⋊Dic3—21no—
206C2×C3⋊Dic3—21no—
207C2×C3⋊Dic3—21no—
208C2×C3⋊Dic3—21no—
209C2×C3⋊Dic3—21no—
210C2×C3⋊Dic3—21no—
211C2×C3⋊Dic3—21no—
212C2×C3⋊Dic3—21no—
213C2×C3⋊Dic3—21no—
214C2×C3⋊Dic3—21no—
215C2×C3⋊Dic3—21no—
216C2×C3⋊Dic3—21no—
217C2×C3⋊Dic3—21no—
218C2×C3⋊Dic3—21no—
219C2×C3⋊Dic3—21no—
220C2×C3⋊Dic3—44no—
221C2×C3⋊Dic3—44no—
222C2×C3⋊Dic3—44no—
223C2×C3⋊Dic3#4112yes—
224C2×#121C3⋊D311yescharacteristic
225C2×C4×D4—91no—
226#400—91no—
227#397—91no—
228#397—91no—
229#394—91no—
230#388—91no—
231#387—91no—
232#386—91no—
233#386—91no—
234#386—91no—
235#386—91no—
236#385—91no—
237#381—91no—
238C2×#95—91no—
239C24×C3C22×D314yes—
240C24×C3C22×D314yes—
241C24×C3C22×D314yes—
242C2×C3×D4—28no—
243C2×C3×D4—28no—
244C2×C3×D4—28no—
245C2×C3×D4—28no—
246C2×C3×D4—28no—
247C2×C3×D4—28no—
248C2×C3×D4—28no—
249C2×C3×D4—44no—
250C2×C3×D4#67116yes—
251C22×C3×C4—28no—
252C22×C3×C4—28no—
253C22×C3×C4—44no—
254C22×C3×C4C22×D314yes—
255C22×C3×C4C22×D314yes—
256C22×C3×C4C22×D314yes—
257C22×C3×C4C22×D314yes—
258C22×Dic3—34no—
259C22×Dic3—34no—
260C22×Dic3—34no—
261C22×Dic3—34no—
262C22×Dic3—34no—
263C22×Dic3—34no—
264C22×Dic3—34no—
265C22×Dic3—34no—
266C22×Dic3—68no—
267C22×Dic3—68no—
268C22×Dic3—68no—
269C22×Dic3—68no—
270C22×Dic3—68no—
271C22×Dic3—124no—
272C22×Dic3—124no—
273C22×Dic3—124no—
274C22×Dic3—124no—
275C3×C4⋊C4—28no—
276C3×C22⋊C4—28no—
277C3×C22⋊C4—28no—
278#217—68no—
279#217—68no—
280#217—68no—
281#217—68no—
282#217—124no—
283#217—124no—
284#217—124no—
285#217—124no—
286#217—124no—
287C4⋊Dic3—68no—
288Dic3⋊C4—68no—
289Dic3⋊C4—124no—
290C4×Dic3—68no—
291C22×C32—22no—
292C22×C32—22no—
293C22×C32—22no—
294C22×C32—22no—
295C22×C32—22no—
296C22×C32—22no—
297C22×C32—22no—
298C22×C32—22no—
299C22×C32—22no—
300C22×C32—41no—
301C22×C32—41no—
302C22×C32—41no—
303C22×C32—41no—
304C22×C32—41no—
305C22×C32—41no—
306C22×C32—41no—
307C22×C32—41no—
308C22×C32—41no—
309C22×C32—41no—
310C22×C32—41no—
311C22×C32#12314yes—
312C22×C32C22×D411yescharacteristic
313C22×C32C2×#4111yescharacteristic
314C22×C32C2×#4111yescharacteristic
315C22×C32C2×#4111yescharacteristic
316C22×C32C2×#4111yescharacteristic
317C22×C32H(5,𝔽2)11yescharacteristic
318C22×C32H(5,𝔽2)11yescharacteristic
319C32×C4—22no—
320C32×C4—22no—
321C32×C4—41no—
322C32×C4—41no—
323C3⋊Dic3—22no—
324C3⋊Dic3—41no—
325C3⋊Dic3—41no—
326C3⋊Dic3—41no—
327C3⋊Dic3—41no—
328C3⋊Dic3—41no—
329C3⋊Dic3—41no—
330C3⋊Dic3—41no—
331C22×D4C2×C3⋊D311yescharacteristic
332C22×D4C2×C3⋊D311yescharacteristic
333C22×D4C2×C3⋊D311yescharacteristic
334C23×C4—91no—
335C23×C4—91no—
336C23×C4—91no—
337C23×C4C2×C3⋊D311yescharacteristic
338#121—24no—
339C4×D4—184no—
340C2×C4⋊C4—91no—
341C2×C4⋊C4—91no—
342C2×C4⋊C4—91no—
343C2×C4⋊C4C2×C3⋊D311yescharacteristic
344C2×C22⋊C4—91no—
345C2×C22⋊C4—91no—
346C2×C22⋊C4—91no—
347C2×C22⋊C4—91no—
348C2×C22⋊C4—91no—
349C2×C22⋊C4—91no—
350C2×C22⋊C4—91no—
351C2×C22⋊C4—91no—
352C2×C22⋊C4—91no—
353C2×C22⋊C4C2×C3⋊D311yescharacteristic
354C2×C22⋊C4C2×C3⋊D311yescharacteristic
355C2×C42—91no—
356#95—91no—
357#95—91no—
358#95—91no—
359#95—91no—
360#95—91no—
361#95—91no—
362#95—91no—
363#95—91no—
364#95—91no—
365#95—91no—
366#95—91no—
367#95—91no—
368C23×C3—24no—
369C23×C3—24no—
370C23×C3—24no—
371C23×C3—24no—
372C23×C3—24no—
373C23×C3—24no—
374C23×C3—24no—
375C23×C3—24no—
376C23×C3—24no—
377C23×C3—24no—
378C23×C3—24no—
379C23×C3—24no—
380C23×C3—24no—
381C23×C3—24no—
382C23×C3—24no—
383C23×C3—24no—
384C23×C3—24no—
385C23×C3#23718yes—
386C23×C3#23718yes—
387C23×C3C2×#6718yes—
388C23×C3C2×#6718yes—
389C23×C3C23×D314yes—
390C3×D4—232no—
391C3×D4—416no—
392C3×D4—416no—
393C2×C3×C4—24no—
394C2×C3×C4—24no—
395C2×C3×C4—24no—
396C2×C3×C4—24no—
397C2×C3×C4—24no—
398C2×C3×C4—24no—
399C2×C3×C4—24no—
400C2×C3×C4—24no—
401C2×C3×C4—24no—
402C2×C3×C4—24no—
403C2×C3×C4—416no—
404C2×C3×C4#23718yes—
405C2×C3×C4C2×#6718yes—
406C2×Dic3—38no—
407C2×Dic3—64no—
408C2×Dic3—64no—
409C2×Dic3—64no—
410C2×Dic3—64no—
411C2×Dic3—64no—
412C2×Dic3—64no—
413C2×Dic3—64no—
414C2×Dic3—64no—
415C2×Dic3—64no—
416C2×Dic3—64no—
417C2×Dic3—64no—
418C2×Dic3—64no—
419C2×Dic3—64no—
420C2×Dic3—64no—
421C2×Dic3—64no—
422C2×Dic3—64no—
423C2×Dic3—64no—
424C2×Dic3—64no—
425C2×Dic3—64no—
426C2×Dic3—64no—
427C2×Dic3—64no—
428C2×Dic3—64no—
429C2×Dic3—64no—
430C2×Dic3—1216no—
431C2×Dic3—1216no—
432C2×Dic3—1216no—
433C2×C32—24no—
434C2×C32—42no—
435C2×C32—81no—
436C2×C32C2×#12311yescharacteristic
437C2×C32#52911yescharacteristic
438C2×C32#53811yescharacteristic
439C2×C32#54611yescharacteristic
440C2×C32#54611yescharacteristic
441C2×C32#55311yescharacteristic
442C2×C32#55311yescharacteristic
443C24C22×C3⋊D311yescharacteristic
444C24C22×C3⋊D311yescharacteristic
445C24C22×C3⋊D311yescharacteristic
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—41no—
454C2×D4#63814yes—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—41no—
458C22×C4—91no—
459C22×C4—91no—
460C22×C4—91no—
461C22×C4—91no—
462C22×C4—91no—
463C22×C4—91no—
464C22×C4—91no—
465C22×C4—91no—
466C22×C4—182no—
467C22×C4—182no—
468C22×C4—182no—
469C22×C4—182no—
470C22×C4—182no—
471C22×C4—361no—
472C22×C4—361no—
473C22×C4—361no—
474C22×C4—361no—
475C22×C4C22×C3⋊D311yescharacteristic
476C22×C4C22×C3⋊D311yescharacteristic
477C22×C4C22×C3⋊D311yescharacteristic
478C22×C4C22×C3⋊D311yescharacteristic
479C4⋊C4—22no—
480C4⋊C4—182no—
481C4⋊C4—182no—
482C4⋊C4—361no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—182no—
486C22⋊C4—182no—
487C22⋊C4—182no—
488C22⋊C4—182no—
489C22⋊C4—361no—
490C22⋊C4—361no—
491C22⋊C4—361no—
492C22⋊C4—361no—
493C22⋊C4—361no—
494C42—182no—
495C22×C3—28no—
496C22×C3—28no—
497C22×C3—28no—
498C22×C3—28no—
499C22×C3—28no—
500C22×C3—28no—
501C22×C3—28no—
502C22×C3—28no—
503C22×C3—28no—
504C22×C3—44no—
505C22×C3—44no—
506C22×C3—44no—
507C22×C3—44no—
508C22×C3—44no—
509C22×C3—44no—
510C22×C3—44no—
511C22×C3—44no—
512C22×C3—44no—
513C22×C3—44no—
514C22×C3—44no—
515C22×C3#935116yes—
516C22×C3C2×#23714yes—
517C22×C3C2×#23714yes—
518C22×C3C2×#23714yes—
519C22×C3#100414yes—
520C22×C3D3×#4114yes—
521C22×C3#100914yes—
522C22×C3C22×#6714yes—
523C3×C4—28no—
524C3×C4—28no—
525C3×C4—44no—
526C3×C4—44no—
527Dic3—68no—
528Dic3—124no—
529Dic3—124no—
530Dic3—124no—
531Dic3—124no—
532Dic3—124no—
533Dic3—124no—
534Dic3—124no—
535C32#244411yescharacteristic, complemented, Sylow
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23#383012yes—
554C23#383012yes—
555C23C2×#63812yes—
556C23C2×#63812yes—
557C23C23×C3⋊D311yescharacteristic
558D4—28no—
559D4—44no—
560D4—44no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—44no—
572C2×C4—92no—
573C2×C4—181no—
574C2×C4—181no—
575C2×C4—181no—
576C2×C4—181no—
577C2×C4—181no—
578C2×C4—181no—
579C2×C4—181no—
580C2×C4—181no—
581C2×C4—181no—
582C2×C4—181no—
583C2×C4—181no—
584C2×C4—181no—
585C2×C4—181no—
586C2×C4—181no—
587C2×C4—181no—
588C2×C4—181no—
589C2×C4—181no—
590C2×C4—181no—
591C2×C4—181no—
592C2×C4—181no—
593C2×C4—181no—
594C2×C4—181no—
595C2×C4—181no—
596C2×C4—364no—
597C2×C4—364no—
598C2×C4—364no—
599C2×C4#383012yes—
600C2×C4C2×#63812yes—
601C2×C3—216no—
602C2×C3—48no—
603C2×C3—84no—
604C2×C3#560014yes—
605C2×C3#560114yes—
606C2×C3#561714yes—
607C2×C3#561814yes—
608C2×C3C2×#93514yes—
609C2×C3#580614yes—
610C2×C3#582914yes—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22#6414414yes—
632C22C2×#383011yescharacteristic
633C22C2×#383011yescharacteristic
634C22C2×#383011yescharacteristic
635C22#6436111yescharacteristic
636C22#41×C3⋊D311yescharacteristic
637C22#6436611yescharacteristic
638C22C22×#63811yescharacteristic
639C4—22no—
640C4—22no—
641C4—41no—
642C4—41no—
643C4—182no—
644C4—361no—
645C4—361no—
646C4—361no—
647C4—361no—
648C4—361no—
649C4—361no—
650C4—361no—
651C3#8265614yescomplemented
652C2—24no—
653C2—42no—
654C2—81no—
655C2#1059607111yescharacteristic
656C2#1059607211yescharacteristic
657C2#1059608811yescharacteristic
658C2#1059608911yescharacteristic
659C2C2×#6414411yescharacteristic
660C2#1059627711yescharacteristic
661C2#1059630011yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
Fitting, prime radicalC2×C32×#121C2
hypercenterC2×#121C3⋊D3
hypocenterC32#2444
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×#121

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×D4×C3⋊Dic3C2semidirect
3. #10592921C2semidirect
4. #10592919C2semidirect
5. #10592919C2semidirect
6. #10592919C2semidirect
7. #10592919C2semidirect
8. #10592909C2semidirect
9. C2×#63658C2semidirect
10. #10592685C2semidirect
11. #10592677C2semidirect
12. #10592652C2semidirect
13. #10592651C2semidirect
14. #10592643C2semidirect
15. #10592642C2semidirect
535. C32#2444semidirect
651. C3#82656semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C32×#1212
C2×D4×C3⋊Dic32
#105929212
#105929192
#105929092
C2×#636582
#105926852
#105926772
#105926522
#105926512
#105926432
#105926422
#826563